Landa P.S.

Noice-induced phase transitions and turbulence
P.S. Landa
Moscow State University, Russia

It is hypothesized that the transition to turbulence in nonclosed flows and formation of coherent structures associated with it is not excitation of self-oscillations, first periodic and then chaotic, as is commonly adopted by many investigators after the works by Landau, Stuart, Ruelle and Takens [1-3], but a noise-induced nonequilibrium phase transition. Such transitions are known for some systems (see, for example [4-6]). Molecular structure of the medium is a source of the noise. This hypothesis is supported by a number of numerical experiments [7].

As an example we have considered in detail the noise-induced phase transition in a pendulum with a randomly vibrating suspension axis. This transition is consist in the excitation of pendulum's oscillations owing to the random vibration. It is akin to parametrical excitation of pendulum's oscillations by a harmonic force. The oscillations excited are reminiscent in form of chaotic self-oscillations appearing in a dynamical system as a result of intermittency. The correlation dimension for these oscillations is finite. A single criterion that allows us to distinguish such the oscillations from dynamical chaos is the Rytov-Dimentberg criterion [8,9].

1. L.D. Landau, DAN SSSR, 44 (1944) 339 (in Russian).
2. J.T. Stuart, J. Fluid Mech., 4 (1958) 1; 9 (1960) 353.
3. D. Ruelle and F. Takens, Math. Phys., 20 (1971) 167.
4. W. Horsthemke and R. Lefever, Noise-Induced Transitions, (Springer-Verlag, Berlin, 1984).
5. C. Van den Broeck, J.M.R. Parrondo, and R. Toral, Phys. Rev. Lett., 73 (1994) 3395.
6. J.M.R. Parrondo, C. Van den Broeck, J. Buceta, and F. de la Rubia, Phisica A, to appear.
7. N.V. Nikitin, DAN, 343 (1995) 767 (in Russian).
8. S.M. Rytov, Introduction to Statistical Radiophysics, (Moscow, Nauka, 1966) (in Russian).
9. M.F. Dimentberg, Nonlinear Stochastic Problems of Mechanical Oscillations, (Moscow, Nauka, 1980) (in Russian).